Covering graphs of various types of finite partially ordered sets have been extensively studied since Ore in [2] asked for a characterization of such graphs in general. In this note we introduce a graph, called the m-chain graph of a poset, that reduces to the covering graph when m = 1. Since we will show how to construct the m-chain graph for m > 2 as the 2-chain graph of another poset, we are...

The paper presents a graphical characterization of the largest chain graphs which serve as unique representatives of classes of Markov equivalent chain graphs. The characterization is a basis for an algorithm constructing, for a given chain graph, the largest chain graph equivalent to it. The algorithm was used to generate a catalog of the largest chain graphs with at most ve vertices. Every it...